Function Expression :
\[f(x)=\frac{(x+1 )e^{-x}}{\sqrt{x+1}} \]Domain
\[\left]-1, \infty\right[ \]Limits
\[\lim_{x \overset{>}{\rightarrow-1} }f(x) = 0 \]\[\lim_{x \rightarrow+\infty}f(x) = 0 \]
\[ \]
Derivate
\[f^{\,\prime}(x)=\frac{- \left(x + 1\right) e^{- x} + e^{- x}}{\sqrt{x + 1}} - \frac{e^{- x}}{2 \sqrt{x + 1}} \]\[f^{\,\prime}(x)=\frac{\left(- x - \frac{1}{2}\right) e^{- x}}{\sqrt{x + 1}} \]
\[f^{\,\prime}(x)=\frac{\left(- 2 x - 1\right) e^{- x}}{2 \sqrt{x + 1}} \]
Integral
\[F(x) = e \left(- \sqrt{x + 1} e^{- x - 1} - \frac{\sqrt{\pi} \operatorname{erfc}{\left(\sqrt{x + 1} \right)}}{2}\right) \]Sign Table
Variation Table
Plot
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